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Given a pre-trained classifier and multiple human experts, we investigate the task of online classification where model predictions are provided for free but querying humans incurs a cost. In this practical but under-explored setting, oracle ground truth is not available. Instead, the prediction target is defined as the consensus vote of all experts. Given that querying full consensus can be costly, we propose a general framework for online Bayesian consensus estimation, leveraging properties of the multivariate hypergeometric distribution. Based on this framework, we propose a family of methods that dynamically estimate expert consensus from partial feedback by producing a posterior over expert and model beliefs. Analyzing this posterior induces an interpretable trade-off between querying cost and classification performance. We demonstrate the efficacy of our framework against a variety of baselines on CIFAR-10H and ImageNet-16H, two large-scale crowdsourced datasets. 

Abstract We present a global survey of energetic electron precipitation from the equatorial magnetosphere due to hiss waves in the plasmasphere and plumes. Using Van Allen Probes measurements, we calculate the pitch angle diffusion coefficients at the bounce loss cone, and evaluate the energy spectrum of precipitating electron flux. Our ∼6.5‐year survey shows that, during disturbed times, hiss inside the plasmasphere primarily causes the electron precipitation atL > 4 over 8 h < MLT < 18 h, and hiss waves in plumes cause the precipitation atL > 5 over 8 h < MLT < 14 h andL > 4 over 14 h < MLT < 20 h. The precipitating energy flux increases with increasing geomagnetic activity, and is typically higher in the plasmaspheric plume than the plasmasphere. The characteristic energy of precipitation increases from ∼20 keV atL = 6–∼100 keV atL = 3, potentially causing the loss of electrons at several hundred keV.